Titanites

Well, they like to play tug-of-war (otherwise known as "pull the stick", and you'd be surprised how strong a small octopus can be.

Some people like to skip small shells along the bottom for the octo to chase, and then there are hide and seek games. Or run your fingers along the outside of the tank and your octo will chase them. Lots more... you get the idea!

Titanites

One more thing I forgot - you could get a small cleaning magnet - the kind with one part on the inside of the tank, and one part on the outside.
Ollie thought that was fun, both when we moved it around and she chased it, and when she came over and pulled of the part in the water, took it back to her den and hid it!

GPO

my octo like to tug on the feeder stick at feeding time, although sometimes i wonder if it is playing with my, it seems pretty aggressive when it sarts tugging, sometimes it will take another arm and grab a rock to pull against